= Magnetic susceptibility tensor
{title2=$\chi_{ij}=\partial M_i/\partial H_j$}
A <magnetic susceptibility tensor> maps a small change of internal <magnetic field intensity> to a change of <magnetization>:
$$
\delta M_i=\sum_j\chi_{ij}\,\delta H_{{\rm int},j}.
$$
This <tensor> reduces to $\chi\delta_{ij}$ for <isotropy>. With <anisotropy>, even a linear response need not point along the applied <magnetic field intensity>. As a stipulated example, $\boldsymbol\chi=\operatorname{diag}(1,1,3)\times10^{-4}$ sends $(H,0,H)$ to $(H,0,3H)\times10^{-4}$. State the axes and bias field when reporting its components. A constant <tensor> describes linear response; in a nonlinear material it is the <Jacobian matrix> of the response at the chosen operating point.
Back to article page